Radiometry and
Photometry
Wei-Chih Wang
Department of Power Mechanical Engineering
National TsingHua University
W. Wang
Materials Covered
• Radiometry
- Radiant Flux
- Radiant Intensity
- Irradiance
- Radiance
• Photometry
- luminous Flux
- luminous Intensity
- Illuminance
- luminance
Conversion from radiometric and photometric
W. Wang
Radiometry
Radiometry is the detection
and measurement of light
waves in the optical portion of
the electromagnetic spectrum
which is further divided into
ultraviolet, visible, and infrared
light.
Example of a typical radiometer
3
W. Wang
Photometry
All light measurement is
considered radiometry
with photometry being a
special subset of
radiometry weighted for a
typical human eye
response.
Example of a typical photometer
4
W. Wang
Human Eyes
Figure shows a schematic illustration of the human eye (Encyclopedia
Britannica, 1994).
The inside of the eyeball is clad by the retina, which is the light-sensitive
part of the eye. The illustration also shows the fovea, a cone-rich central
region of the retina which affords the high acuteness of central vision.
Figure also shows the cell structure of the retina including the
light-sensitive rod cells and cone cells. Also shown are the ganglion cells
and nerve fibers that transmit the visual information to the brain. Rod cells
are more abundant and more light sensitive than cone cells. Rods are
5
sensitive over the entire visible spectrum.
W. Wang
There are three types of cone cells, namely cone cells
sensitive in the red, green, and blue spectral range. The
approximate spectral sensitivity functions of the rods and
three types or cones are shown in the figure above
6
W. Wang
Eye sensitivity function
The conversion between radiometric and photometric units is provided by
the luminous efficiency function or eye sensitivity function, V(λ). The
CIE 1978 V(λ) function, which can be considered the most accurate
description of the eye sensitivity in the photopic vision regime
7
W. Wang
Scotopic and Photopic filter
Use of a photopic correction filter is important when measuring the perceived
brightness of a source to a human. The filter weights incoming light in proportion to
the effect it would produce in the human eye. Regardless of the color or spectral
distribution of the source, the photopic detector can deliver accurate illuminance
and luminance measurements in a single reading. Scotopic vision refers to the
eye’s dark-adapted sensitivity (night vision).
W. Wang
The table summarizes the most common radiometric
and photometric quantities.
W. Wang
Conversion
To convert between radiometric and photometric units, one needs to know the
photopic spectral luminous efficiency curve V(), which gives the spectral
response of the human eye to various wavelengths of light. The original curve,
which is shown earlier, was adopted by the Commission on Illumination (CIE)
as the standard in 1924 and is still used today even though modifications have
been suggested. Empirical data shows that the curve has a maximum value of
unity at 555nm, which is the wavelength of light at which the human eye is
most sensitive, and trails off to levels below 10-5 for wavelengths below 370nm
and above 780nm.
The lumen (lm) is the photometric equivalent of the watt, weighted to match
the eye response of the “standard observer”. Yellowish-green light receives
the greatest weight because it stimulates the eye more than blue or red light of
equal radiometric power:
1 watt at 555 nm = 683.0 lumens
QUANTITY
RADIOMETRIC
Power
W
Power Per Unit Area
W/m2
Power Per Unit Solid Angle
W/sr
Per Unit Area Per Unit Solid Angle W/m2·sr
PHOTOMETRIC
Lumen (lm) = cd·sr
Lux (lx) = cd·sr/m2 = lm/m2
Candela (cd) Power
cd/m2 = lm/m2·sr = nit
W. Wang
Conversion
The conversion between photometric units which take into
account human physiology and straight radiometric units is
given by the following:(photometric unit) = (radiometric unit)
x (683) x V()where V() is the 'Photopic Response,' shown
earlier and basically tells us how efficiently the eye picks up
certain wavelengths of light. The Photopic response is a
function of the wavelength of light and so to convert from
radiometric units to photometric units first requires
knowledge of the light source. If the source is specified as
having a certain color temperature we can assume that its
spectral radiance emittance is the same as a perfect black
body radiator and use Planck’s law.
W. Wang
Conversion
A non-linear regression fit to the experimental data yields the approximation,
where the wavelength is in micrometers.
According to the definition for a candela, there are 683 lumens per watt for
555nm light that is propagating in a vacuum. Hence, for a monochromatic light
source, it is fairly simple to convert from watts to lumens; simply multiply
the power in watts by the appropriate V() value, and use the conversion factor
from the definition for a candela.
For example, the photometric power of a 5mW red ( = 650nm) laser pointer,
which corresponds to V() = 0.096, is 0.096 x 0.005W x 683lm/W = 0.33lm,
whereas the value for a 5mW green ( = 532nm) laser pointer is 0.828 x 0.005W
x 683lm/W = 2.83lm. Thus, although both laser pointers have the exact same
radiant flux, the green laser pointer will appear approximately 8.5 times brighter
than the red one assuming both have the same beam diameter.
W. Wang
Conversion
Conversion from radiometric to photometric units becomes more complex if the light
source is not monochromatic. In this case, the mathematical quantity of interest is
where v is the luminous flux in lumens, Km is a scaling factor equal to 683 lumens per
watt, E() is the spectral power in watts per nanometer, and V() is the photopic spectral
luminous efficiency function. Note that the integration is only carried out over the
wavelengths for which V() is non-zero (i.e. = 380 - 830nm). Since V() is given by a
table of empirical values, it is best to do the integration numerically.
W. Wang
Radiometric power is converted to
luminous flux via the integral equation.
V( is the spectral response of the human
eye in daylight, otherwise known as the
photopic curve. The unit of luminous flux is
the lumen.
W. Wang
Example
Artificial sources in general do not have the same spectral distribution as a perfect
black body but for our purposes we shall consider them equal. The graph above
depicts the spectral radiance of several black body radiators. If we consider the
Photopic evaluation of a black body radiation at a temperature of T=2045K.
Integration of the product of the light emittance by the Photopic function provides the
conversion from a Radiometric signal to a Photometric.
W. Wang
Graphic depiction of conversion

W. Wang
Radiant Intensity and luminous Intensity
Solid angle is the 3 dimensional analog of an ordinary angle. In the
figure, the edge of a circular disk, the bright red circle, is projected to
the center of a sphere. The projection intersects the sphere and forms
a surface area A. Solid angle is the area A on the surface of a sphere
of radius R divided by the radius squared. The units of solid angle are
steradians. Note that it is a dimensionless quantity.
W. Wang
Radiance and Luminance measurement
Projected solid angle takes into account the projected
area when the viewpoint is other than the center of the
sphere. The element of solid angle is shown in red. The
area of projected solid angle is shown in blue.
W. Wang
As an example, the projected solid angle
for a cone of half angle alpha is calculated.
W. Wang
LED Example
A Lambertian source is defined as one in
which the brightness (or
luminance) is independent of angle, in
other words the off-axis luminance is
the same as on-axis. Such a source has an
intensity vs. angle profile that
falls off as the cosine of the angle.
Historically, many LED sources have had
nearly Lambertian beam distributions,
simplifying certain calculations.
W. Wang
LED Example
Take the example of calculating the
luminous flux within a certain cone
angle. Substituting the intensity
distribution of a Lambertian source
into the equation makes the
integration simple. For a so-called
Lambertian LED, the total lumens is
about 3 times the on-axis intensity.
W. Wang
Radiant Flux 
Radiant flux is the fundamental unit in detector-based radiometry. It is defined as the total optical
power of a light source, and is expressed in watts.
To measure radiant flux, the detector must collect all emitted light. Examples of typical flux
measurements are shown in Figure 2. Focused lasers and fiber optic cables require only the
proper sensor head because the source and detector can be configured so that all radiation is
incident within the active area of the sensor. Diverging light sources, such as LEDs and lamps,
may require an integrating sphere to capture light radiating in several directions.
Radiant Intensity (I = dd)
Radiant Intensity is the amount of flux emitted through a known solid angle. It is measured in
watts/steradian.
To measure radiant intensity, start with the angle subtended by the detector at a given distance
from the source (see Figure 4). Then divide the amount of flux by that solid angle.
Radiant Intensity is a property of the light source and may not be relevant if the spatial
distribution of radiation from the source is non-uniform. It is appropriate for point sources (and for
close approximations, such as an LED intensity measurements), but not for collimated sources.
Irradiance (E=/A = 4I /4r2 = I/r2)
Irradiance is the amount of radiant flux incident on a known surface area. Its international unit of
measure is watt/m2. However, because many sensor heads have a 1-cm2 detector area, it is
simpler to use watt/cm2.
There are two ways to control the size of the detector area. The first is to use a sensor head with
a known detector area. The second is to place an aperture with a known area between the source
and the detector. When source radiation does not completely fill the detector, an aperture is the
only reliable method of controlling detector area.
Radiance (L= dI/ dAcos)
Radiance is the radiant intensity emitted from a known unit area of a source. Units of radiance
are used to describe extended light sources, such as a CRT or an EL/O Panel unit for
characterizing point sources.
To measure radiance, you need to define the area of the source to be measured, and also the
solid angle received. This is usually simulated using an aperture and a positive lens in front of
the detector. It is expressed as watts/cm2·ster.
W. Wang
of intensity are
lumens per solid
angle, or
steradians
Illuminance,
is “light falling
on a surface”,
with units of
lumens per
area
Luminance is “light from a surface in a
direction”. The units are lumens per area per
solid angle; it is the perceived brightness.
W. Wang
Quantity
Name
Unit
Symbol[nb 1]
Radiant energy
Qe
Radiant energy
density
we
Radiant flux
[nb 2]
Φe[nb 2]
[nb 3]
Spectral flux
Φe,ν
or
Φe,λ[nb 4]
Name
Dimension
Notes
Symbol
Symbol
joule
J
M⋅L2⋅T−2
Energy of
electromagnetic
radiation.
joule per cubic
metre
J/m3
M⋅L−1⋅T−2
Radiant energy per unit
volume.
W or J/s
M⋅L2⋅T−3
Radiant energy
emitted, reflected,
transmitted or
received, per unit time.
This is sometimes also
called "radiant power".
W/Hz
or
W/m
M⋅L2⋅T−2
watt
watt per hertz
or
watt per metre
or
M⋅L⋅T−3
Radiant flux per unit
frequency or
wavelength. The latter
is commonly measured
in W⋅sr−1⋅m−2⋅nm−1.
W. Wang
Radiant intensity
Ie,Ω[nb 5]
Ie,Ω,ν[nb 3]
Spectral intensity or
Ie,Ω,λ[nb 4]
Radiance
Le,Ω[nb 5]
Le,Ω,ν[nb 3]
Spectral radiance or
Le,Ω,λ[nb 4]
watt per steradian W/sr
watt per steradian
per hertz
W⋅sr−1⋅Hz−1
or
or
watt per steradian W⋅sr−1⋅m−1
per metre
watt per steradian
W⋅sr−1⋅m−2
per square metre
watt per steradian
per square metre
per hertz
W⋅sr−1⋅m−2⋅Hz−1
or
or
watt per steradian W⋅sr−1⋅m−3
per square metre,
per metre
M⋅L2⋅T−3
Radiant flux emitted,
reflected, transmitted or
received, per unit solid
angle. This is a
directional quantity.
M⋅L2⋅T−2
or
M⋅L⋅T−3
Radiant intensity per
unit frequency or
wavelength. The latter is
commonly measured in
W⋅sr−1⋅m−2⋅nm−1. This is
a directional quantity.
M⋅T−3
Radiant flux emitted,
reflected, transmitted or
received by a surface,
per unit solid angle per
unit projected area. This
is a directional quantity.
This is sometimes also
confusingly called
"intensity".
M⋅T−2
or
M⋅L−1⋅T−3
Radiance of a surface
per unit frequency or
wavelength. The latter is
commonly measured in
W⋅sr−1⋅m−2⋅nm−1. This is
a directional
W. Wang
Irradiance
Ee[nb 2]
[nb 3]
Ee,ν
Spectral irradiance or
Ee,λ[nb 4]
Radiosity
Je[nb 2]
[nb 3]
Je,ν
Spectral radiosity or
Je,λ[nb 4]
watt per square
metre
watt per square
metre per hertz
or
watt per square
metre, per metre
watt per square
metre
watt per square
metre per hertz
or
watt per square
metre, per metre
W/m2
W⋅m−2⋅Hz−1
or
W/m3
W/m2
W⋅m−2⋅Hz−1
or
W/m3
M⋅T−3
Radiant flux received by a
surface per unit area. This
is sometimes also
confusingly called
"intensity".
M⋅T−2
or
M⋅L−1⋅T−3
Irradiance of a surface per
unit frequency or
wavelength. The terms
spectral flux density or
more confusingly "spectral
intensity" are also used.
Non-SI units of spectral
irradiance include Jansky =
10−26 W⋅m−2⋅Hz−1 and solar
flux unit (1SFU = 10−22
W⋅m−2⋅Hz−1).
M⋅T−3
Radiant flux leaving
(emitted, reflected and
transmitted by) a surface
per unit area. This is
sometimes also confusingly
called "intensity".
M⋅T−2
or
M⋅L−1⋅T−3
Radiosity of a surface per
unit frequency or
wavelength. The latter is
commonly measured in
W⋅m−2⋅nm−1. This is
sometimes also confusingly
called "spectral intensity".
W. Wang
Radiant exitance
Me[nb 2]
Me,ν[nb 3]
Spectral exitance or
Me,λ[nb 4]
watt per square
metre
watt per square
metre per hertz
or
watt per square
metre, per metre
Radiant exposure He
joule per square
metre
He,ν[nb 3]
Spectral exposure or
He,λ[nb 4]
joule per square
metre per hertz
or
joule per square
metre, per metre
W/m2
W⋅m−2⋅Hz−1
or
W/m3
J/m2
J⋅m−2⋅Hz−1
or
J/m3
M⋅T−3
Radiant flux emitted by a
surface per unit area. This is
the emitted component of
radiosity. "Radiant emittance"
is an old term for this quantity.
This is sometimes also
confusingly called "intensity".
M⋅T−2
or
M⋅L−1⋅T−3
Radiant exitance of a surface
per unit frequency or
wavelength. The latter is
commonly measured in
W⋅m−2⋅nm−1. "Spectral
emittance" is an old term for
this quantity. This is sometimes
also confusingly called
"spectral intensity".
M⋅T−2
Radiant energy received by a
surface per unit area, or
equivalently irradiance of a
surface integrated over time of
irradiation. This is sometimes
also called "radiant fluence".
M⋅T−1
or
M⋅L−1⋅T−2
Radiant exposure of a surface
per unit frequency or
wavelength. The latter is
commonly measured in
J⋅m−2⋅nm−1. This is sometimes
also called "spectral fluence".
W. Wang
Hemispherical
ε
emissivity
Spectral
εν
hemispherical or
emissivity
ελ
Directional
emissivity
Spectral
directional
emissivity
εΩ
εΩ,ν
or
εΩ,λ
1
Radiant exitance of a
surface, divided by that
of a black body at the
same temperature as
that surface.
1
Spectral exitance of a
surface, divided by that
of a black body at the
same temperature as
that surface.
1
Radiance emitted by a
surface, divided by that
emitted by a black
body at the same
temperature as that
surface.
1
Spectral radiance
emitted by a surface,
divided by that of a
black body at the same
temperature as that
surface.
W. Wang
Hemispherical
absorptance
Spectral
hemispherical
absorptance
Directional
absorptance
Spectral
directional
absorptance
A
Aν
or
Aλ
AΩ
AΩ,ν
or
AΩ,λ
1
Radiant flux absorbed by a
surface, divided by that received
by that surface. This should not
be confused with "absorbance".
1
Spectral flux absorbed by a
surface, divided by that received
by that surface. This should not
be confused with "spectral
absorbance".
1
Radiance absorbed by a
surface, divided by the radiance
incident onto that surface. This
should not be confused with
"absorbance".
1
Spectral radiance absorbed by a
surface, divided by the spectral
radiance incident onto that
surface. This should not be
confused with "spectral
absorbance".
W. Wang
Hemispherical
reflectance
R
Spectral
hemispherical
reflectance
Rν
or
Rλ
Directional
reflectance
RΩ
Spectral
directional
reflectance
RΩ,ν
or
RΩ,λ
1
Radiant flux reflected by a
surface, divided by that
received by that surface.
1
Spectral flux reflected by a
surface, divided by that
received by that surface.
1
Radiance reflected by a
surface, divided by that
received by that surface.
1
Spectral radiance reflected
by a surface, divided by
that received by that
surface.
W. Wang
Hemispherical
transmittance
T
Spectral
hemispherical
transmittance
Tν
or
Tλ
Directional
transmittance
TΩ
Spectral
directional
transmittance
TΩ,ν
or
TΩ,λ
1
Radiant flux transmitted
by a surface, divided by
that received by that
surface.
1
Spectral flux transmitted
by a surface, divided by
that received by that
surface.
1
Radiance transmitted by a
surface, divided by that
received by that surface.
1
Spectral radiance
transmitted by a surface,
divided by that received
by that surface.
W. Wang
Hemispherical
attenuation
coefficient
Spectral
hemispherical
attenuation
coefficient
Directional
attenuation
coefficient
Spectral
directional
attenuation
coefficient
μ
μν
or
μλ
μΩ
μΩ,ν
or
μΩ,λ
reciprocal metre m−1
reciprocal metre m−1
reciprocal metre m−1
reciprocal metre m−1
L−1
Radiant flux absorbed and
scattered by a volume per
unit length, divided by that
received by that volume.
L−1
Spectral radiant flux
absorbed and scattered
by a volume per unit
length, divided by that
received by that volume.
L−1
Radiance absorbed and
scattered by a volume per
unit length, divided by that
received by that volume.
L−1
Spectral radiance
absorbed and scattered
by a volume per unit
length, divided by that
received by that volume.
W. Wang
1.^ Standards organizations recommend that radiometric quantities should be denoted
with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
2.^ Jump up to: a b c d e Alternative symbols sometimes seen: W or E for radiant energy,
P or F for radiant flux, I for irradiance, W for radiant exitance.
3.^ Jump up to: a b c d e f g Spectral quantities given per unit frequency are denoted with
suffix "ν" (Greek)—not to be confused with suffix "v" (for "visual") indicating a
photometric quantity.
4.^ Jump up to: a b c d e f g Spectral quantities given per unit wavelength are denoted with
suffix "λ" (Greek).
5.^ Jump up to: a b Directional quantities are denoted with suffix "Ω" (Greek).
W. Wang
Quantity
Unit
Symbol
Name
[nb 1]
Luminous energy
Luminous flux /
luminous power
Notes
Symbol
Symbol
Qv [nb 2] lumen second
lm⋅s
T⋅J [nb 3]
Units are sometimes called talbots.
Φv [nb 2] lumen (= cd⋅sr)
lm
J [nb 3]
Luminous energy per unit time.
candela (= lm/sr)
cd
J [nb 3]
Luminous power per unit solid angle.
L−2⋅J
Luminous power per unit solid angle per
unit projected source area. Units are
sometimes called nits.
Luminous intensity Iv
Name
Dimension
Luminance
Lv
candela per square metre
cd/m2
Illuminance
Ev
lux (= lm/m2)
lx
L−2⋅J
Luminous power incident on a surface.
Luminous exitance
/ luminous
Mv
emittance
lux
lx
L−2⋅J
Luminous power emitted from a surface.
Luminous exposure Hv
lux second
lx⋅s
L−2⋅T⋅J
Luminous energy
density
ωv
lumen second per cubic
metre
lm⋅s⋅m−3 L−3⋅T⋅J
Luminous efficacy
η [nb 2]
lumen per watt
lm/W
Luminous efficiency
/ luminous
V
coefficient
M−1⋅L−2⋅T3⋅ Ratio of luminous flux to radiant flux or
J
power consumption, depending on context.
1
W. Wang
Radiometric Measurement
•Radiant Flux Measurements (in units of watts) are performed with an instrument
known as a flux meter or optical power meter. This type of testing is typically used for
characterizing the total output of sources such as:Lasers, LEDs, Lamps and FiberOptic Systems
•Radiant Intensity Measurements (in units of W/sr) are performed with an
instrument that may be described as an optical intensity meter. This type of testing is
typically used for characterizing the output of a relatively small source in a particular
direction. Typical devices under test include: LEDs, UV Lamps and IR Lamps
•Irradiance Measurements (in units of W/m2) are performed with an irradiance
meter. This involves the measurement of the radiant flux incident upon a surface, per
unit area. Such measurements are important in the following fields: Medical,
Biological and Remote Sensing
•Radiance Measurements (in units of W/m2sr) are performed with a radiance meter.
This involves measuring the light emitted in a particular direction by a given spot on
the surface of an extended source. Such measurements are important in fields such
as: Remote Sensing, Avionics and Night Vision
W. Wang
Radiometers
Radiometers. Radiometers are used to
measure the amount of electromagnetic energy
present within a specific wavelength range. The
measurement is expressed in Watts (W) which
is a unit of measurement for power.
Radiometers are usually used to detect and
measure the amount of energy outside the
visible light spectrum and are used to measure
ultraviolet (UV) light or infrared (IR). A typical
use for a UV meter is in the museum lighting
world where the presence of UV is can be very
troublesome. UV energy hastens the ageing
process due to its higher energy content so any
energy below 400nm needs to be filtered out or
eliminated. Another application for a radiometer
is in the detection and measurement of infrared
or IR. It is used to detect and measure heat on
a surface. Technicians use them to safely detect
and repair overheating motors or shorted out
wiring. Radiometers can measure very quickly
because they are simple meters that use only
one sensor with a filter designed to just
measure the wavelength range they were
intended for.
W. Wang
First Radiometer
The radiometer is made from a glass bulb
from which much of the air has been
removed to form a partial vacuum. Inside
the bulb, on a low friction spindle, is a rotor
with several (usually four) vertical
lightweight metal vanes spaced equally
around the axis. The vanes are polished or
white on one side and black on the other.
When exposed to sunlight, artificial light, or
infrared radiation (even the heat of a hand
nearby can be enough), the vanes turn with
no apparent motive power, the dark sides
retreating from the radiation source and the
light sides advancing.
Cooling the radiometer causes rotation in
the opposite direction.
W. Wang
Photometric Measurement
Photometric measurement is based on photodetectors, devices (of several types) that
produce an electric signal when exposed to light. Simple applications of this technology
include switching luminaires on and off based on ambient light conditions, and light
meters, used to measure the total amount of light incident on a point.
More complex forms of photometric measurement are used frequently within the lighting
industry. Spherical photometers can be used to measure the directional luminous flux
produced by lamps, and consist of a large-diameter globe with a lamp mounted at its
center. A photocell rotates about the lamp in three axes, measuring the output of the
lamp from all sides.
Lamps and lighting fixtures are tested using goniophotometers and rotating mirror
photometers, which keep the photocell stationary at a sufficient distance that the
luminaire can be considered a point source. Rotating mirror photometers use a
motorized system of mirrors to reflect light emanating from the luminaire in all directions
to the distant photocell; goniophotometers use a rotating 2-axis table to change the
orientation of the luminaire with respect to the photocell. In either case, luminous
intensity is tabulated from this data and used in lighting design.
W. Wang
Goniophotometers
A Goniophotometer is a device used for measurement of the light
emitted from an object at different angles.[1] The use of
goniophotometers has been increasing in recent years with the
introduction of LED-light sources, which are mostly directed light
sources, where the spatial distribution of light is not homogeneous.[2] If
a light source is homogeneous in its distribution of light, it is called a
Lambertian source.[3] Due to strict regulations, the spatial distribution of
light is of high importance to automotive lighting and its design.
W. Wang
Spherical photometers
Luminous flux measurement is to
determine the total visible energy emitted
by a light source. An integrating sphere is
often used to converge all the power
emitted by the source to the detector head.
W. Wang
Handheld Photometer
W. Wang
Silicon Detector with Flat Response Filter
Since silicon photodiodes are more sensitive to light at the red end of the spectrum
than to light at the blue end, radiometric detectors filter the incoming light to even out
the responsivity, producing a “flat response”. This is important for accurate
radiometric measurements, because the spectrum of a light source may be
unknown, or may be dependent on operating conditions such as input voltage.
W. Wang
Blackbody Radiation
Blackbody radiation" or "cavity radiation" refers to an object or system which absorbs all
radiation incident upon it and re-radiates energy which is characteristic of this radiating
system only, not dependent upon the type of radiation which is incident upon it. The
radiated energy can be considered to be produced by standing wave or resonant modes
of the cavity which is radiating
W. Wang